Fair point, Nik. Moreover I myself used to say that a typical word is 
the dependent of just one word, but exceptionally a finite verb is the 
dependent of either one or zero words. Moreover, if we allow reciprocal 
relations such as parent/child, as soon as we allow the value of one 
relation to have a quantity, it automatically follows that the argument 
of the other must have a quantity too. OK. I was wrong, and either term 
(arg or val) of a property can have a quantity. Sorry folks - fallibity 
strikes again. Hope none of you catch it from me.

Dick

Nikolas Gisborne wrote:
> Dear All,
> I agree with And that there don't seem to be any obvious reasons by the 
> arguments of relations can't be quantified. I expected someone to come 
> back to me and say something like this:
> 
> (1) In a cognitive system we model propositional knowledge.
> (2) The propositional knowledge being modelled includes our knowledge 
> about what we know.
> (3) If we know that Dick has 2 daughters we can show that has has two 
> daughters.
> (4) Knowing that Dick has 2 daughters isn't the same as knowing 
> 'daughter1 = Lucy' and 'daughter2 = Alice' so we can state something like
> 
> (i) Dick<--arg--(daughter)--val-->[quant:2]
> 
> without knowing who the daughters are or anything about them.
> 
> (5) Likewise, we can make the same proposition if we know everything 
> there is to be known about Lucy and Alice. In that case, (i) is a 
> general statement of our propositional knowledge in a relationship to 
> (ii) and (iii) but not equivalent to them, or to the conjunction of 
> them, and actually involving a different 'daughter' relation.
> 
> (ii) Dick<--arg--(daughter)--val-->Lucy
> (iii) Dick<--arg--(daughter)--val-->Alice
> 
> (6) We could also say something like (iv)
> 
> (iv) Dick<--arg--(daughter)--val-->[set: (member1=Lucy); (member2=Alice)]
> 
> (7) But (iv) is a way of re-representing (ii) and (iii), not of 
> re-representing (i).
> (8) Therefore, my discussion yesterday about Brigham Young's wives was 
> orthogonal to the issue of whether arguments of relations can have a 
> quantified expression or not.
> (9) The following proposition is true.
> 
> (v) [set: (member1=Dick); (member2=Gay)] <---arg--(daughter)--val--->Lucy
> 
> (10) and the proposition in (vi) is a way of stating our knowledge of 
> (v) without being a restatement of (v).
> 
> (vi) [quant:2]<---arg--(daughter)--val--->Lucy
> 
> where (vi) says 'Lucy is the daughter of two parents'.
> 
> Therefore, there doesn't appear to be any obvious reason why the 
> arguments of WG relations shouldn't also be quantified/counted.
> 
> Furthermore, imagine a child -- call him Bert -- who is the child of a 
> father, an egg-donating mother, and a separate birth-mother. We might 
> want to say Bert is the child of three parents. (vii) is a way of 
> showing that.
> 
> (vii) [quant:3]<---arg--(child)--val--->Bert
> 
> (11) To put it another way (viii) is a way of saying 'X has N of these 
> relation-entities'
> 
> (viii) X<--arg--(relation)--val-->[quant=N]
> 
> and (ix) is a way of saying 'N of these relation-entities have X'
> 
> (ix) [quant:N]<--arg--(relation)--val-->X
> 
> Like And, I can't see any reason to say that arguments can't have 
> quantities. After all, about 28000 people in Scotland have (newly 
> diagnosed) cancer each year. '28000 people in Scotland have cancer' has 
> the structure of (ix), no?
> 
> Nik.
> 
> 
> 
> 2009/12/15 Nikolas Gisborne <[log in to unmask] 
> <mailto:[log in to unmask]>>
> 
>     And:
> 
> 
>     I fully accept your conclusions about there being not only multiple
>     wives but also multiple spousal relations. And I think we will
>     probably agree that relations are individuated by their
>     arguments/relata, so that if you have a one-to-n mapping, there are
>     n relations.
> 
> 
>         But does this support Dick's contention about the
>         cognitive/theoretical basis for the argument/value distinction?
> 
> 
>     If it means we can't say:
> 
>     BY <--val--(husband of)--arg-->[>1]
> 
>     Or whatever the notation is. Can we?
> 
>     Nik.
> 
> 

-- 
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